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Mixed integer linear programming (MILP) solvers expose hundreds of parameters that have an outsized impact on performance but are difficult to configure for all but expert users. Existing machine learning (ML) approaches require training on…
In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and…
Mixed-integer linear programming (MILP) plays a crucial role in artificial intelligence, biochemistry, finance, cryptography, etc. Notwithstanding popular for decades, the researches of MILP solvers are still limited by the resource…
While Mixed-integer linear programming (MILP) is NP-hard in general, practical MILP has received roughly 100--fold speedup in the past twenty years. Still, many classes of MILPs quickly become unsolvable as their sizes increase, motivating…
In many operational applications, it is necessary to routinely find, within a very limited time window, provably good solutions to challenging mixed-integer linear programming (MILP) problems. An example is the Security-Constrained Unit…
With the accelerated development of Industry 4.0, intelligent manufacturing systems increasingly require efficient task allocation and scheduling in multi-robot systems. However, existing methods rely on domain expertise and face challenges…
Machine Learning models are increasingly used for decision making, in particular in high-stakes applications such as credit scoring, medicine or recidivism prediction. However, there are growing concerns about these models with respect to…
Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving…
We transform join ordering into a mixed integer linear program (MILP). This allows to address query optimization by mature MILP solver implementations that have evolved over decades and steadily improved their performance. They offer…
This applied research article explores the application of Mixed-Integer Linear Programming (MILP) to address line-balancing challenges in the garment industry, focusing on optimizing production processes under multiple constraints. By…
Primal heuristics play a critical role in improving the efficiency of mixed integer programming (MILP) solvers. As large language models (LLMs) have demonstrated superior code generation abilities, recent MILP works are devoted to…
Maintaining instantaneous balance between electricity supply and demand is critical for reliability and grid instability. System operators achieve this through solving the task of Unit Commitment (UC),ca high dimensional large-scale…
We address the optimal design of a large scale multi-agent system where each agent has discrete and/or continuous decision variables that need to be set so as to optimize the sum of linear local cost functions, in presence of linear local…
Combinatorial sequential decision making problems are typically modeled as mixed integer linear programs (MILPs) and solved via branch and bound (B&B) algorithms. The inherent difficulty of modeling MILPs that accurately represent…
Markov Decision Processes (MDPs) are stochastic optimization problems that model situations where a decision maker controls a system based on its state. Partially observed Markov decision processes (POMDPs) are generalizations of MDPs where…
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks…
Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), as they significantly tighten the dual bounds and improve the solving performance. A key problem for cuts is when to stop cuts generation, which…
This paper focuses on the problem of supplying the workstations of assembly lines with components during the production process. For that specific problem, this paper presents a Mixed Integer Linear Program (MILP) that aims at minimizing…
A mathematical programming model for a class of single machine family scheduling problem is described in this technical report, with the aim of comparing the performance in solving the scheduling problem by means of mathematical programming…
A common challenge in real-time operations is deciding whether to re-solve an optimization problem or continue using an existing solution. While modern data platforms may collect information at high frequencies, many real-time operations…